About the geometric mean calculator
The geometric mean is the n-th root of the product of n positive numbers. It’s the right average for things that multiply: growth rates, investment returns, ratios, aspect ratios and scale factors. Enter numbers separated by spaces, commas or new lines.
Switch on growth-rate mode to enter percentage changes (e.g. 10, −5, 20): the calculator averages the growth factors 1.10, 0.95, 1.20 and reports the equivalent constant rate, the same idea as CAGR.
Formulas
| Geometric mean | G = (x₁·x₂·…·xₙ)^(1/n) |
| Arithmetic mean | A = (x₁ + … + xₙ)/n |
| Harmonic mean | H = n/(1/x₁ + … + 1/xₙ) |
| Inequality | min ≤ H ≤ G ≤ A ≤ max |
Frequently asked questions
Why use the geometric mean instead of the average?
For quantities that compound. If an investment gains 50% then loses 50%, the arithmetic average is 0%, but you actually lost 25%. The geometric mean of the factors (1.5 × 0.5)^½ = 0.866 correctly gives −13.4% per period.
Can the geometric mean use negative numbers?
Not in general, the product could be negative and have no real root. Use growth-rate mode for percentage changes instead.